NeurIPS 2018 Papers

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discretization error can dominate when we are near the boundary of the space. We demonstrate that because of this, current SGMCMC methods for the simplex struggle with sparse simplex spaces; when many of the components are close to zero. Unfortunately, many popular large-scale Bayesian models, such as network or topic models, require inference on sparse simplex spaces. To avoid the biases caused by this discretization error, we propose the stochastic Cox-Ingersoll-Ross process (SCIR), which removes all discretization error and we prove that samples from the SCIR process are asymptotically unbiased. We discuss how this idea can be extended to target other constrained spaces. Use of the SCIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.

Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not Hilbertian. Indeed, this was recently exemplified in a string of papers which show that the simple task of averaging a few PDs can be computationally prohibitive. We propose in this article a tractable framework to carry out standard tasks on PDs at scale, notably evaluating distances, estimating barycenters and performing clustering. This framework builds upon a reformulation of PD metrics as optimal transport (OT) problems. Doing so, we can exploit recent computational advances: the OT problem on a planar grid, when regularized with entropy, is convex can be solved in linear time using the Sinkhorn algorithm and convolutions. This results in scalable computations that can stream on GPUs. We demonstrate the efficiency of our approach by carrying out clustering with diagrams metrics on several thousands of PDs, a scale never seen before in the literature.

We present a formulation of deep learning that aims at producing a large margin classifier. The notion of \emc{margin}, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any $l_p$ norm ($p \geq 1$) on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random/adversarial input transform) and regularization techniques such as weight decay, dropout, and batch norm. \footnote{Code for the large margin loss function is released at \url{https://github.com/google-research/google-research/tree/master/large_margin}}

We present a novel deep architecture and a training strategy to learn a local feature pipeline from scratch, using collections of images without the need for human supervision. To do so we exploit depth and relative camera pose cues to create a virtual target that the network should achieve on one image, provided the outputs of the network for the other image. While this process is inherently non-differentiable, we show that we can optimize the network in a two-branch setup by confining it to one branch, while preserving differentiability in the other. We train our method on both indoor and outdoor datasets, with depth data from 3D sensors for the former, and depth estimates from an off-the-shelf Structure-from-Motion solution for the latter. Our models outperform the state of the art on sparse feature matching on both datasets, while running at 60+ fps for QVGA images.

We propose a stepsize adaptation scheme for stochastic gradient descent. It operates directly with the loss function and rescales the gradient in order to make fixed predicted progress on the loss. We demonstrate its capabilities by conclusively improving the performance of Adam and Momentum optimizers. The enhanced optimizers with default hyperparameters consistently outperform their constant stepsize counterparts, even the best ones, without a measurable increase in computational cost. The performance is validated on multiple architectures including dense nets, CNNs, ResNets, and the recurrent Differential Neural Computer on classical datasets MNIST, fashion MNIST, CIFAR10 and others.

Knowledge distillation is effective to train the small and generalisable network models for meeting the low-memory and fast running requirements. Existing offline distillation methods rely on a strong pre-trained teacher, which enables favourable knowledge discovery and transfer but requires a complex two-phase training procedure. Online counterparts address this limitation at the price of lacking a high-capacity teacher. In this work, we present an On-the-fly Native Ensemble (ONE) learning strategy for one-stage online distillation. Specifically, ONE only trains a single multi-branch network while simultaneously establishing a strong teacher on-the-fly to enhance the learning of target network. Extensive evaluations show that ONE improves the generalisation performance of a variety of deep neural networks more significantly than alternative methods on four image classification dataset: CIFAR10, CIFAR100, SVHN, and ImageNet, whilst having the computational efficiency advantages.

As an indispensable component, Batch Normalization (BN) has successfully improved the training of deep neural networks (DNNs) with mini-batches, by normalizing the distribution of the internal representation for each hidden layer. However, the effectiveness of BN would diminish with the scenario of micro-batch (e.g. less than 4 samples in a mini-batch), since the estimated statistics in a mini-batch are not reliable with insufficient samples. This limits BN's room in training larger models on segmentation, detection, and video-related problems, which require small batches constrained by memory consumption. In this paper, we present a novel normalization method, called Kalman Normalization (KN), for improving and accelerating the training of DNNs, particularly under the context of micro-batches. Specifically, unlike the existing solutions treating each hidden layer as an isolated system, KN treats all the layers in a network as a whole system, and estimates the statistics of a certain layer by considering the distributions of all its preceding layers, mimicking the merits of Kalman Filtering. On ResNet50 trained in ImageNet, KN has 3.4% lower error than its BN counterpart when using a batch size of 4; Even when using typical batch sizes, KN still maintains an advantage over BN while other BN variants suffer a performance degradation. Moreover, KN can be naturally generalized to many existing normalization variants to obtain gains, e.g. equipping Group Normalization with Group Kalman Normalization (GKN). KN can outperform BN and its variants for large scale object detection and segmentation task in COCO 2017.

Knowledge distillation (KD) aims to train a lightweight classifier suitable to provide accurate inference with constrained resources in multi-label learning. Instead of directly consuming feature-label pairs, the classifier is trained by a teacher, i.e., a high-capacity model whose training may be resource-hungry. The accuracy of the classifier trained this way is usually suboptimal because it is difficult to learn the true data distribution from the teacher. An alternative method is to adversarially train the classifier against a discriminator in a two-player game akin to generative adversarial networks (GAN), which can ensure the classifier to learn the true data distribution at the equilibrium of this game. However, it may take excessively long time for such a two-player game to reach equilibrium due to high-variance gradient updates. To address these limitations, we propose a three-player game named KDGAN consisting of a classifier, a teacher, and a discriminator. The classifier and the teacher learn from each other via distillation losses and are adversarially trained against the discriminator via adversarial losses. By simultaneously optimizing the distillation and adversarial losses, the classifier will learn the true data distribution at the equilibrium. We approximate the discrete distribution learned by the classifier (or the teacher) with a concrete distribution. From the concrete distribution, we generate continuous samples to obtain low-variance gradient updates, which speed up the training. Extensive experiments using real datasets confirm the superiority of KDGAN in both accuracy and training speed.

Convolutional neural networks (CNNs) have recently achieved great success in single-image super-resolution (SISR). However, these methods tend to produce over-smoothed outputs and miss some textural details. To solve these problems, we propose the Super-Resolution CliqueNet (SRCliqueNet) to reconstruct the high resolution (HR) image with better textural details in the wavelet domain. The proposed SRCliqueNet firstly extracts a set of feature maps from the low resolution (LR) image by the clique blocks group. Then we send the set of feature maps to the clique up-sampling module to reconstruct the HR image. The clique up-sampling module consists of four sub-nets which predict the high resolution wavelet coefficients of four sub-bands. Since we consider the edge feature properties of four sub-bands, the four sub-nets are connected to the others so that they can learn the coefficients of four sub-bands jointly. Finally we apply inverse discrete wavelet transform (IDWT) to the output of four sub-nets at the end of the clique up-sampling module to increase the resolution and reconstruct the HR image. Extensive quantitative and qualitative experiments on benchmark datasets show that our method achieves superior performance over the state-of-the-art methods.

Recent models for learned image compression are based on autoencoders that learn approximately invertible mappings from pixels to a quantized latent representation. The transforms are combined with an entropy model, which is a prior on the latent representation that can be used with standard arithmetic coding algorithms to generate a compressed bitstream. Recently, hierarchical entropy models were introduced as a way to exploit more structure in the latents than previous fully factorized priors, improving compression performance while maintaining end-to-end optimization. Inspired by the success of autoregressive priors in probabilistic generative models, we examine autoregressive, hierarchical, and combined priors as alternatives, weighing their costs and benefits in the context of image compression. While it is well known that autoregressive models can incur a significant computational penalty, we find that in terms of compression performance, autoregressive and hierarchical priors are complementary and can be combined to exploit the probabilistic structure in the latents better than all previous learned models. The combined model yields state-of-the-art rate-distortion performance and generates smaller files than existing methods: 15.8% rate reductions over the baseline hierarchical model and 59.8%, 35%, and 8.4% savings over JPEG, JPEG2000, and BPG, respectively. To the best of our knowledge, our model is the first learning-based method to outperform the top standard image codec (BPG) on both the PSNR and MS-SSIM distortion metrics.

We consider the problem of active feature acquisition where the goal is to sequentially select the subset of features in order to achieve the maximum prediction performance in the most cost-effective way at test time. In this work, we formulate this active feature acquisition as a jointly learning problem of training both the classifier (environment) and the RL agent that decides either to

This paper introduces a model-based reinforcement learning (MBRL) framework that incorporates the underlying decision problem in learning the transition model of the environment. This is in contrast with conventional approaches to MBRL that learn the model of the environment, for example by finding the maximum likelihood estimate, without taking into account the decision problem. Value-Aware Model Learning (VAML) framework argues that this might not be a good idea, especially if the true model of the environment does not belong to the model class from which we are estimating the model. The original VAML framework, however, may result in an optimization problem that is difficult to solve. This paper introduces a new MBRL class of algorithms, called Iterative VAML, that benefits from the structure of how the planning is performed (i.e., through approximate value iteration) to devise a simpler optimization problem. The paper theoretically analyzes Iterative VAML and provides finite sample error upper bound guarantee for it.

Model-free reinforcement learning (RL) algorithms directly parameterize and update value functions or policies, bypassing the modeling of the environment. They are typically simpler, more flexible to use, and thus more prevalent in modern deep RL than model-based approaches. However, empirical work has suggested that they require large numbers of samples to learn. The theoretical question of whether not model-free algorithms are in fact \emph{sample efficient} is one of the most fundamental questions in RL. The problem is unsolved even in the basic scenario with finitely many states and actions. We prove that, in an episodic MDP setting, Q-learning with UCB exploration achieves regret $\tlO(\sqrt{H^3 SAT})$ where $S$ and $A$ are the numbers of states and actions, $H$ is the number of steps per episode, and $T$ is the total number of steps. Our regret matches the optimal regret up to a single $\sqrt{H}$ factor. Thus we establish the sample efficiency of a classical model-free approach. Moreover, to the best of our knowledge, this is the first model-free analysis to establish $\sqrt{T}$ regret \emph{without} requiring access to a ``simulator.''

In this work, we present new theoretical results on convolutional generative neural networks, in particular their invertibility (i.e., the recovery of input latent code given the network output). The study of network inversion problem is motivated by image inpainting and the mode collapse problem in training GAN. Network inversion is highly non-convex, and thus is typically computationally intractable and without optimality guarantees. However, we rigorously prove that, under some mild technical assumptions, the input of a two-layer convolutional generative network can be deduced from the network output efficiently using simple gradient descent. This new theoretical finding implies that the mapping from the low- dimensional latent space to the high-dimensional image space is bijective (i.e., one-to-one). In addition, the same conclusion holds even when the network output is only partially observed (i.e., with missing pixels). Our theorems hold for 2-layer convolutional generative network with ReLU as the activation function, but we demonstrate empirically that the same conclusion extends to multi-layer networks and networks with other activation functions, including the leaky ReLU, sigmoid and tanh.

Representations of data that are invariant to changes in specified factors are useful for a wide range of problems: removing potential biases in prediction problems, controlling the effects of covariates, and disentangling meaningful factors of variation. Unfortunately, learning representations that exhibit invariance to arbitrary nuisance factors yet remain useful for other tasks is challenging. Existing approaches cast the trade-off between task performance and invariance in an adversarial way, using an iterative minimax optimization. We show that adversarial training is unnecessary and sometimes counter-productive; we instead cast invariant representation learning as a single information-theoretic objective that can be directly optimized. We demonstrate that this approach matches or exceeds performance of state-of-the-art adversarial approaches for learning fair representations and for generative modeling with controllable transformations.

We present a novel introspective variational autoencoder (IntroVAE) model for synthesizing high-resolution photographic images. IntroVAE is capable of self-evaluating the quality of its generated samples and improving itself accordingly. Its inference and generator models are jointly trained in an introspective way. On one hand, the generator is required to reconstruct the input images from the noisy outputs of the inference model as normal VAEs. On the other hand, the inference model is encouraged to classify between the generated and real samples while the generator tries to fool it as GANs. These two famous generative frameworks are integrated in a simple yet efficient single-stream architecture that can be trained in a single stage. IntroVAE preserves the advantages of VAEs, such as stable training and nice latent manifold. Unlike most other hybrid models of VAEs and GANs, IntroVAE requires no extra discriminators, because the inference model itself serves as a discriminator to distinguish between the generated and real samples. Experiments demonstrate that our method produces high-resolution photo-realistic images (e.g., CELEBA images at (1024^{2})), which are comparable to or better than the state-of-the-art GANs.

We present a new algorithm to generate minimal, stable, and symbolic corrections to an input that will cause a neural network with ReLU activations to change its output. We argue that such a correction is a useful way to provide feedback to a user when the network's output is different from a desired output. Our algorithm generates such a correction by solving a series of linear constraint satisfaction problems. The technique is evaluated on three neural network models: one predicting whether an applicant will pay a mortgage, one predicting whether a first-order theorem can be proved efficiently by a solver using certain heuristics, and the final one judging whether a drawing is an accurate rendition of a canonical drawing of a cat.

Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks is fundamentally difficult as the structure of representations varies greatly, even across groups of networks trained on identical tasks, and over the course of training. Here, we develop projection weighted CCA (Canonical Correlation Analysis) as a tool for understanding neural networks, building off of SVCCA, a recently proposed method (Raghu et al, 2017). We first improve the core method, showing how to differentiate between signal and noise, and then apply this technique to compare across a group of CNNs, demonstrating that networks which generalize converge to more similar representations than networks which memorize, that wider networks converge to more similar solutions than narrow networks, and that trained networks with identical topology but different learning rates converge to distinct clusters with diverse representations. We also investigate the representational dynamics of RNNs, across both training and sequential timesteps, finding that RNNs converge in a bottom-up pattern over the course of training and that the hidden state is highly variable over the course of a sequence, even when accounting for linear transforms. Together, these results provide new insights into the function of CNNs and RNNs, and demonstrate the utility of using CCA to understand representations.

Given two candidate models, and a set of target observations, we address the problem of measuring the relative goodness of fit of the two models. We propose two new statistical tests which are nonparametric, computationally efficient (runtime complexity is linear in the sample size), and interpretable. As a unique advantage, our tests can produce a set of examples (informative features) indicating the regions in the data domain where one model fits significantly better than the other. In a real-world problem of comparing GAN models, the test power of our new test matches that of the state-of-the-art test of relative goodness of fit, while being one order of magnitude faster.